Licensed shared access is a new frequency sharing concept that allows Mobile Network Operators (MNOs) to use some of the spectrum initially allocated to other incumbents, after obtaining a temporary license from the regulator. The allocation is made among groups such that two base stations in the same group can use the same spectrum simultaneously. In this context, different auction schemes were proposed, however they consider the scenario in which the regulator has one and only one block of LSA frequency to allocate. In this paper, we remove this hypothesis: we suppose that the regulator has K identical blocks of spectrum to allocate, and we propose a truthful auction mechanism based on the Vickrey-Clarke- Groves mechanism (VCG).We evaluate the efficiency of our mechanism in terms of social welfare, which depends on the allocation rule of the mechanism. Simulations show that the efficiency of the proposed mechanism is at least 60 % of that of VCG, which is known to be optimal.